Yes, if you have performed a proper assessment of catheter patency - flushed with a 10 mL syringe and met no resistance plus obtained a brisk blood return without any difficulty. The issue is not simply the syringe size, although smaller syringes are known to generate greater amounts of pressure inside the catheter lumen. However, this pressure will ***only*** reach a level that would produce catheter damage ***if*** you are meeting resistance. No resistance means no increase in pressure. Also, what is the purpose of having a stopcock on that catheter hub? These are well-known to increase the risk of bloodstream infections.